In Exercises 27–42, solve each formula for the specified variable.Do you recognize the formula? If so, what does it describe?27. I = Prt for P28. C = 2ar for r30. P = C + MC for M32. A = th(a + b) for b29. T = D + pm for p31. A = h(a + b) for a%3D33. S = P + Prt for r34. S = P + Prt for tFfor SS - VC36. S =35. В %3D1 -r37. IR + Ir = E for I38. A = 2lw + 2lh + 2wh for h1139. - +1140.R R R1=- for ffor Rfih-for fifi + 2fifzfor f2fi + 241. f =42. f =

As there are multiple questions, 27 is solved here.

Answered: In Exercises 27–42, solve each formula…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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In Exercises 43–46, solve each formula for the specified variable. 3V for V Th 43. r = 44. r = A for A 45. t = 2T . for l 32 46. v = FR for m m
In Exercises 31–32, solve each formula for the specified variable. 1 31. V = - lwh for h 3 32. Ax + By = C for y
For Exercises 49–52, rewrite the equation so that the coefficient on x is positive.
In Exercises 49–54, solve for y in terms of t or x, as appropriate.
Exercises 7–12: Determine whether the equation is linear or nonlinear by trying to write it in the form ax + b = 0. 7. 3x – 1.5 = 7
America is getting older. The graph shows the projected elderly U.S. population for ages 65–84 and for ages 85 and older.The formula E = 5.8√x + 56.4 models the projected number of elderly Americans ages 65–84, E, in millions, x years after 2020.a. Use the formula to find the projected increase in the number of Americans ages 65–84, in millions, from 2030 to 2060. Express this difference in simplified radicalform.b. Use a calculator and write your answer in part (a) to the nearest tenth. Does this rounded decimal overestimate or underestimate the difference in the projected data shown by the bar graph ? By how much?
In Exercises 43–54, solve each absolute value equation or indicate the equation has no solution. 43. |x – 2| = 7 45. |2x – 1| = 5 47. 2|3x – 2| = 14 44. |x + 1| = 5 46. |2r – 3| = 11 48. 3|2x – 1| = 21 %3D %3D 5 24 - + 6 = 18 50. 4 1 x + 7 = 10 51. |x + 1| + 5 = 3 53. |2x – 1| + 3 = 3 52. |x + 1| + 6 = 2 54. |3x – 2| + 4 = 4
In Exercises 1–6, solve for x.
For Exercises 33–42, solve the equation on the interval [0, 2π). (See Examples 5–7)
In Exercises 23–25, solve each equation. If the solution set is Ø or (-0, ), classify the equation as an inconsistent equation or an identity. 23. 3(2x – 4) = 9 – 3(x + 1) 2x 24. x - 4 x + 1 4 2 4 25. 3(x – 4) + x = 2(6 + 2x)
Solve the variation problems in Exercises 68–73. 68. A company's profit varies directly as the number of products it sells. The company makes a profit of $1175 on the sale of 25 products. What is the company's profit when it sells 105 products? 69. The distance that a body falls from rest varies directly as the square of the time of the fall. If skydivers fall 144 feet in 3 seconds, how far will they fall in 10 seconds? 70. The pitch of a musical tone varies inversely as its wavelength. A tone has a pitch of 660 vibrations per second and a wavelength of 1.6 feet. What is the pitch of a tone that has a wavelength of 2.4 feet? 71. The loudness of a stereo speaker, measured in decibels, varies inversely as the square of your distance from the speaker. When you are 8 feet from the speaker, the loudness is 28 decibels. What is the loudness when you are 4 feet from the speaker? 72. The time required to assemble computers varies directly as the number of computers assembled and inversely as…
For Exercises 33–38, find the exact value of each expression without the use of a calculator. (See Example 5)

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